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Preface
I. DESCRIPTIVE STATISTICS
1. Introduction to Statistics
Stumbling Blocks to Statistics
A Brief Look at the History of Statistics
Gertrude Cox (1900-1978)
Benefits of a Course in Statistics
General
Fields of Statistics
Summary
Key Terms and Names
Problems
2. Percentages, Graphs and Measures of Central Tendency
Percentage Changes-Comparing Increases with Decreases
Graphs
Measures of Central Tendency
Appropriate Use of the Mean
the Median and the Mode
Summary
Key Terms
Problems
Computer Problems
3. Variability
Measures of Variability
Graphs and Variability
Questionnaire Percentages
Key Terms
Computer Problems
4. The Normal Curve and z Scores
The Normal Curve
z Scores
Carl Friedrich Gauss (1777-1855)
Translating Raw Scores into z Scores
z Score Translation in Practice
Fun with your Calculator
Summary
Key Terms and Names
Problems
5. z Scores Revisited: T Scores and Other Normal Curve Transformations
Other Applications of the z Score
The Percentile Table
T Scores
Normal Cure Equivalents
Stanines
Grade-Equivalent Scores: A Note of Caution
The Importance of the z Score
Summary
Key Terms
Problems
6. Probability
The Definition of Probability
Blaise Pascal (1623-1662)
Probability and Percentage Areas of the Normal Curve
Combining Probabilities for Independent Events
A Reminder about Logic
Summary
Key Terms
Problems
II. INFERENTIAL STATISTICS
7. Statistics and Parameters
Generalizing from the Few to the Many
Key Concepts of Inferential Statistics
Techniques of Sampling
Sampling Distributions
Infinite versus Finite Sampling
Galton and the Concept of Error
Back to z
Some Words of Encouragement
Summary
Key Terms
Problems
8. Parameter Estimates and Hypothesis Testing
Estimating the Population Standard Deviation
Estimating the Standard Error of the Mean
Estimating the Population of the Mean: Interval Estimates and Hypothesis Testing
The t Ratio
The Type 1 Error
Alpha Levels
Effect Size
Interval Estimates: No Hypothesis Test Needed
Summary
Key Terms
Problems
Computer Problems
9. The Fundamentals of Research Methodology
Research Strategies
Independent and Dependent Variables
The Cause-and-Effect Trap
Theory of Measurement
Research: Experimental versus Post Facto
The Experimental Method: The Case of Cause and Effect
Creating Equivalent Groups: The True Experiment
Designing the True Experiment
The Hawthorne Effect
Repeated-Measures Designs with Separate Control Groups
Requirements for the True Experiment
Post Facto-Research
Combination Research
Research Errors
Experimental Errors
Meta-Analysis
Methodology as a Basis for More Sophisticated Techniques
Summary
Key Terms
Problems
10. The Hypothesis of Difference
Sampling Distribution of Differences
Estimated Standard Error of Difference
Two-Sample t Test for Independent Samples
Significance
William Sealy Gossett (1876-1937)
Two-Tailed t Table
Alpha Levels and Confidence Level
The Minimum Difference
Outliner
One-Tail t Test
Importance of Having at Least Two Samples
Power
Effect Size
Summary
Key Terms
Problems
Computer Problems
11. The Hypothesis of Association: Correlation
Cause and Effect
The Pearson r
Interclass versus Intraclass
Karl Pearon (1857-1936)
Missing Data
Correlation Matrix
The Spearman r s’ 293 An Important Difference between the Correlation Correlation Coefficient and t Test
Summary
Key Terms and Names
Problems
Computer Problems
12. Analysis of Variance
Advantages of ANOVA
The Bonferroni Test
Ronald Aylmer, Fisher (1890-1962)
Analyzing the Variance
Applications of ANOVA
The Factorial ANOVA
Eta Square and d
Graphing the Interaction
Summary
Key Terms and Names
Problems
Computer Problems
13. Nominal Data and the Chi Square
Chi Square and Independent Samples
Locating the Difference
Chi Square Percentages
Square and z Scores
Chi Square and Dependent Samples
Requirements for Using Chi Square
Summary
Key Terms
Problems
Computer Problems
III. ADVANCED TOPICS IN INFERENTIAL STATISTICS
14. Regression Analysis
Regression of Y on X
Sir Francis Galton (1822-1911)
Standard Error of Estimate
Multiple R (Linear Regression with More Than Two Variables)
Path Analysis
The Multiple Rand Causation
Partial Correlation
Summary
Key Terms and Names
Computer Problems
15. Repeated-Measures and Matched-Subjects Designs With Interval Data
Problem of Correlated or Dependent Samples
Repeated Measures,
Paired t Ratio
Confidence Interval for Paired Differences
Within-Subjects Effect Size
Testing Correlated Experimental Data
Summary
Key Terms
Problems
Computer Problems
16. Nonparametrics Revisited: The Ordinal Case
Mann-Whitney U Test for Two Ordinal Distributions with Independent Selection
Kruskal-Wallis H Test for Three or More Ordinal Distributions with Independent Selection
Wicoxon T Test for Two Ordinal Distributions with Correlated Selection
Friedman ANOVA By Ranks for Three or More Ordinal Distributions with Correlated Selection
Advantages and Disadvantages of Nonparametric Tests
Summary
Key Terms
Problems
17. Tests and Measurements
Norm and Criterion Referencing: Relative Versus Absolute Performance Measure
The Problem of Bias
Test Reliability
Validityand Measurement Theory
Test Validity
Item Analysis
Summary
Key Terms
Problems
Computer Problems
18. Computers and Statistical Analysis
Computer Literacy
The Statistical Programs
Ada Lovelace (nee Byron, 1815-1852)
Logic Checkpoints
Answers
Recommended Reading
19. Research Simulations: Choosing the Correct Statistical Test
Methodology: Research’s Bottom Line
Checklist Questions
Critical Decision Points
Research Simulations: From A to Z
The Research Enterprise
A Final Thought: The Burden of Proof
Special Unit: The Binomial Case
Special Unit: The Problem of Unequal Variance
Appendix A
Appendix B
Glossary
References
Answers to Odd-Numbered Items (and Within-Chapter Exercises)
Index
Statistical Hall of Fame Biographies
Gertrude Cox-Chapter 1
Carl Gauss-Chapter 4
Blaise Pascal-Chapter 6
William Gossett-Chapter 10
Karl Pearson-Chapter 11
Ronald Fisher-Chapter 12
Sir Francis Galton-Chapter 14
Ada Lovelace-Chapter 18